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Search results for group
34
votes
6
answers
1
GATE CSE 1996 | Question: 1.4
Which of the following statements is FALSE? The set of rational numbers is an abelian group under addition The set of integers in an abelian group under addition The set of rational numbers form an abelian group under multiplication The set of real numbers excluding zero is an abelian group under multiplication
Which of the following statements is FALSE?The set of rational numbers is an abelian group under additionThe set of integers in an abelian group under additionThe set of ...
Kathleen
23.1k
views
Kathleen
asked
Oct 9, 2014
Set Theory & Algebra
gate1996
set-theory&algebra
group-theory
normal
+
–
77
votes
6
answers
2
GATE CSE 2014 Set 3 | Question: 50
There are two elements $x,\:y$ in a group $(G,*)$ such that every element in the group can be written as a product of some number of $x$'s and $y$'s in some order. It is known that $x*x=y*y=x*y*x*y=y*x*y*x=e$ where $e$ is the identity element. The maximum number of elements in such a group is ____.
There are two elements $x,\:y$ in a group $(G,*)$ such that every element in the group can be written as a product of some number of $x$'s and $y$'s in some order. It is ...
go_editor
15.7k
views
go_editor
asked
Sep 28, 2014
Set Theory & Algebra
gatecse-2014-set3
set-theory&algebra
group-theory
numerical-answers
normal
+
–
10
votes
2
answers
3
GATE CSE 2023 | Question: 41
Let $X$ be a set and $2^{X}$ denote the powerset of $X$. Define a binary operation $\Delta$ on $2^{X}$ as follows: \[ A \Delta B=(A-B) \cup(B-A) \text {. } \] Let $H=\left(2^{X}, \Delta\right)$. Which of the following statements about $H$ is/are correct? ... $A \in 2^{X},$ the inverse of $A$ is the complement of $A$. For every $A \in 2^{X},$ the inverse of $A$ is $A$.
Let $X$ be a set and $2^{X}$ denote the powerset of $X$.Define a binary operation $\Delta$ on $2^{X}$ as follows:\[A \Delta B=(A-B) \cup(B-A) \text {. }\]Let $H=\left(2^{...
admin
5.7k
views
admin
asked
Feb 15, 2023
Set Theory & Algebra
gatecse-2023
set-theory&algebra
group-theory
multiple-selects
2-marks
+
–
38
votes
9
answers
4
GATE CSE 2019 | Question: 10
Let $G$ be an arbitrary group. Consider the following relations on $G$: $R_1: \forall a , b \in G, \: a R_1 b \text{ if and only if } \exists g \in G \text{ such that } a = g^{-1}bg$ ... $R_1$ and $R_2$ $R_1$ only $R_2$ only Neither $R_1$ nor $R_2$
Let $G$ be an arbitrary group. Consider the following relations on $G$:$R_1: \forall a , b \in G, \: a R_1 b \text{ if and only if } \exists g \in G \text{ such that } a ...
Arjun
17.4k
views
Arjun
asked
Feb 7, 2019
Set Theory & Algebra
gatecse-2019
engineering-mathematics
discrete-mathematics
set-theory&algebra
group-theory
1-mark
+
–
60
votes
5
answers
5
GATE CSE 2007 | Question: 21
How many different non-isomorphic Abelian groups of order $4$ are there? $2$ $3$ $4$ $5$
How many different non-isomorphic Abelian groups of order $4$ are there?$2$$3$$4$$5$
Kathleen
19.7k
views
Kathleen
asked
Sep 21, 2014
Set Theory & Algebra
gatecse-2007
group-theory
normal
+
–
42
votes
3
answers
6
GATE CSE 1994 | Question: 1.10
Some group $(G, o)$ is known to be abelian. Then, which one of the following is true for $G$? $g=g^{-1} \text{ for every } g \in G$ $g=g^2 \text{ for every }g \in G$ $(goh)^2 = g^2oh^2 \text{ for every } g, h \in G$ $G$ is of finite order
Some group $(G, o)$ is known to be abelian. Then, which one of the following is true for $G$?$g=g^{-1} \text{ for every } g \in G$$g=g^2 \text{ for every }g \in G$$(goh)...
Kathleen
10.7k
views
Kathleen
asked
Oct 4, 2014
Set Theory & Algebra
gate1994
set-theory&algebra
group-theory
normal
+
–
2
votes
2
answers
7
GATE CSE 2024 | Set 2 | Question: 53
Let $Z_{n}$ be the group of integers $\{0,1,2, \ldots, n-1\}$ with addition modulo $n$ as the group operation. The number of elements in the group $Z_{2} \times Z_{3} \times Z_{4}$ that are their own inverses is ___________.
Let $Z_{n}$ be the group of integers $\{0,1,2, \ldots, n-1\}$ with addition modulo $n$ as the group operation. The number of elements in the group $Z_{2} \times Z_{3} \ti...
Arjun
2.1k
views
Arjun
asked
Feb 16
Set Theory & Algebra
gatecse2024-set2
numerical-answers
set-theory&algebra
group-theory
+
–
46
votes
4
answers
8
GATE CSE 1996 | Question: 2.4
Which one of the following is false? The set of all bijective functions on a finite set forms a group under function composition The set $\{1, 2, \dots p-1\}$ forms a group under multiplication mod $p$, where $p$ is a prime number The set of all strings over a finite ... $\langle G, * \rangle$ if and only if for any pair of elements $a, b \in S, a * b^{-1} \in S$
Which one of the following is false?The set of all bijective functions on a finite set forms a group under function compositionThe set $\{1, 2, \dots p-1\}$ forms a group...
Kathleen
9.6k
views
Kathleen
asked
Oct 9, 2014
Set Theory & Algebra
gate1996
set-theory&algebra
normal
set-theory
group-theory
+
–
43
votes
5
answers
9
GATE CSE 2006 | Question: 3
The set $\{1,2,3,5,7,8,9\}$ under multiplication modulo $10$ is not a group. Given below are four possible reasons. Which one of them is false? It is not closed $2$ does not have an inverse $3$ does not have an inverse $8$ does not have an inverse
The set $\{1,2,3,5,7,8,9\}$ under multiplication modulo $10$ is not a group. Given below are four possible reasons. Which one of them is false?It is not closed$2$ does no...
Rucha Shelke
9.9k
views
Rucha Shelke
asked
Sep 16, 2014
Set Theory & Algebra
gatecse-2006
set-theory&algebra
group-theory
normal
+
–
27
votes
4
answers
10
GATE CSE 2010 | Question: 4
Consider the set $S = \{1, ω, ω^2\}$, where $ω$ and $ω^2$ are cube roots of unity. If $*$ denotes the multiplication operation, the structure $(S, *)$ forms A Group A Ring An integral domain A field
Consider the set $S = \{1, ω, ω^2\}$, where $ω$ and $ω^2$ are cube roots of unity. If $*$ denotes the multiplication operation, the structure $(S, *)$ formsA GroupA R...
gatecse
9.9k
views
gatecse
asked
Sep 21, 2014
Set Theory & Algebra
gatecse-2010
set-theory&algebra
normal
group-theory
+
–
1
votes
0
answers
11
Charles C Pinter Abstract Algebra
If G is a group, G=(F(R), +), F(R) set of all real valued functions. H={f€F(R) ; f(-x)=-f(x)} Is H a subgroup of G? My solution.(Click on link..I have not shown th associative prt coz addition is always associative) please let me know if iam correct. https://ibb.co/sPzHg6m https://ibb.co/sPzHg6m
If G is a group, G=(F(R), +), F(R) set of all real valued functions.H={f€F(R) ; f(-x)=-f(x)}Is H a subgroup of G?My solution.(Click on link..I have not shown th associa...
yuyutsu
44
views
yuyutsu
asked
4 days
ago
Set Theory & Algebra
discrete-mathematics
group-theory
+
–
27
votes
4
answers
12
GATE CSE 1995 | Question: 2.17
Let $A$ be the set of all non-singular matrices over real number and let $*$ be the matrix multiplication operation. Then $A$ is closed under $*$ but $\langle A, *\rangle$ is not a semigroup. $\langle A, *\rangle$ is a semigroup but not a monoid. $\langle A, * \rangle$ is a monoid but not a group. $\langle A, *\rangle$ is a a group but not an abelian group.
Let $A$ be the set of all non-singular matrices over real number and let $*$ be the matrix multiplication operation. Then$A$ is closed under $*$ but $\langle A, *\rangle$...
Kathleen
9.9k
views
Kathleen
asked
Oct 8, 2014
Set Theory & Algebra
gate1995
set-theory&algebra
group-theory
+
–
3
votes
1
answer
13
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 28
A group $G$ in which $(a b)^2=a^2 b^2$ for all $a, b$ in $G$ is necessarily finite cyclic abelian none of the above
A group $G$ in which $(a b)^2=a^2 b^2$ for all $a, b$ in $G$ is necessarilyfinitecyclicabeliannone of the above
GO Classes
364
views
GO Classes
asked
Jan 28
Set Theory & Algebra
goclasses2024-mockgate-13
goclasses
set-theory&algebra
group-theory
1-mark
+
–
2
votes
1
answer
14
GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 19
Let $\ast $ be the binary operation on the rational numbers given by $a \ast b=a+b+2 a b$. Which of the following are true? $\ast $ is commutative There is a rational number that is a $\ast \;-$ identity. Every rational number has a $\ast \;-$ inverse. I only I and II only I and III only I, II, and III
Let $\ast $ be the binary operation on the rational numbers given by $a \ast b=a+b+2 a b$. Which of the following are true?$\ast $ is commutativeThere is a rational numbe...
GO Classes
472
views
GO Classes
asked
Jan 21
Set Theory & Algebra
goclasses2024-mockgate-12
goclasses
set-theory&algebra
group-theory
1-mark
+
–
3
votes
0
answers
15
GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 61
Let $S$ be the set of all functions $f: \mathbb{R} \rightarrow \mathbb{R}$. Consider the two binary operations + and $\circ$ on $S$ ... law $(g+h) \circ f=(g \circ f)+(h \circ f)$. None III only II and III only I, II, and III
Let $S$ be the set of all functions $f: \mathbb{R} \rightarrow \mathbb{R}$. Consider the two binary operations + and $\circ$ on $S$ defined as pointwise addition and comp...
GO Classes
439
views
GO Classes
asked
Jan 28
Set Theory & Algebra
goclasses2024-mockgate-13
goclasses
set-theory&algebra
group-theory
2-marks
+
–
2
votes
1
answer
16
GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 37
If $b$ and $c$ are elements in a group $G$, and if $b^5=c^3=e$, where $e$ is the unit element of $G$, then the inverse of $b^2 c b^4 c^2$ must be $b^4 c^2 b^2 c$ $c^2 b^4 c b^2$ $c b^2 c^2 b^4$ $c b c^2 b^3$
If $b$ and $c$ are elements in a group $G$, and if $b^5=c^3=e$, where $e$ is the unit element of $G$, then the inverse of $b^2 c b^4 c^2$ must be$b^4 c^2 b^2 c$$c^2 b^4 c...
GO Classes
436
views
GO Classes
asked
Jan 13
Set Theory & Algebra
goclasses2024-mockgate-11
goclasses
set-theory&algebra
group-theory
2-marks
+
–
0
votes
3
answers
17
UGC NET CSE | June 2008 | Part 2 | Question: 4
The set of positive integers under the operation of ordinary multiplication is : not a monoid not a group a group an Abelian group
The set of positive integers under the operation of ordinary multiplication is :not a monoidnot a groupa groupan Abelian group
admin
299
views
admin
asked
Jan 6
Others
ugcnetcse-june2008-paper2
abelian-group
+
–
40
votes
9
answers
18
GATE CSE 2009 | Question: 22
For the composition table of a cyclic group shown below: ... $a,b$ are generators $b,c$ are generators $c,d$ are generators $d,a$ are generators
For the composition table of a cyclic group shown below:$$\begin{array}{|c|c|c|c|c|} \hline \textbf{*} & \textbf{a}& \textbf{b} &\textbf{c} & \textbf{d}\\\hline \textbf{a...
gatecse
8.9k
views
gatecse
asked
Sep 15, 2014
Set Theory & Algebra
gatecse-2009
set-theory&algebra
normal
group-theory
+
–
14
votes
2
answers
19
GATE CSE 2022 | Question: 17
Which of the following statements is/are $\text{TRUE}$ for a group $\textit{G}?$ If for all $x,y \in \textit{G}, \; (xy)^{2} = x^{2} y^{2},$ then $\textit{G}$ is commutative. If for all $x \in \textit{G}, \; x^{2} = 1,$ then ... $2,$ then $\textit{G}$ is commutative. If $\textit{G}$ is commutative, then a subgroup of $\textit{G}$ need not be commutative.
Which of the following statements is/are $\text{TRUE}$ for a group $\textit{G}?$If for all $x,y \in \textit{G}, \; (xy)^{2} = x^{2} y^{2},$ then $\textit{G}$ is commutati...
Arjun
7.6k
views
Arjun
asked
Feb 15, 2022
Set Theory & Algebra
gatecse-2022
set-theory&algebra
group-theory
multiple-selects
1-mark
+
–
41
votes
2
answers
20
GATE CSE 2014 Set 3 | Question: 3
Let $G$ be a group with $15$ elements. Let $L$ be a subgroup of $G$. It is known that $L \neq\ G$ and that the size of $L$ is at least $4$. The size of $L$ is __________.
Let $G$ be a group with $15$ elements. Let $L$ be a subgroup of $G$. It is known that $L \neq\ G$ and that the size of $L$ is at least $4$. The size of $L$ is __________....
go_editor
8.5k
views
go_editor
asked
Sep 28, 2014
Set Theory & Algebra
gatecse-2014-set3
set-theory&algebra
group-theory
numerical-answers
normal
+
–
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